Enigma 252: Three-point circle

Each of the black dots in the picture is one of the elements — 3 speakers and 22 suppressors — in Uncle Pinkle’s Triphonic Asymmetric Garden Audio-system. The whole square array measures 40 × 40 metres. Uncle Pinkle sits at C, precisely the same distance D from each speaker, but not at distance D from any suppressor; and C must not be directly between any two system-elements, so it isn’t on any of the vertical, horizontal or diagonal lines in the picture. Within these restrictions, Uncle Pinkle has arranged the system-elements and placed his seat so that D is as small as possible.

How far is the distance D? (An answer to the nearest centimetre will do).

This diagram shows one of the 32 possible positions for C. The position C is marked with a large cross, and the three equidistant speakers are marked with circles. The 31 alternative positions for C are marked with smaller crosses.

The example position for C is at (95/7, 85/7) (= 10 × (19/14, 17/14)).

The numbers would have been neater if the grid spacing in Uncle’s array had been, say, 28 ft.
Then the coordinates of C (measured from the corner speaker) would be (34, 38) or (38, 34); and the distance D would be sqrt(2600) which is very close to 51.